1a) If the rate of change, W, is inversely proportional to W(x) where W is always...
1a) If the rate of change, W, is inversely proportional to W(x) where W is always greater than 0. If W(1)=25 and W(4)=17, then find W(0)
1b)assume an object's weight, W, is proportional to its height, H. Does it make sense to use differential equations to model the Weight of the object? If so, write the differential equation. If not, explain why
1c)Assume the population, P, of cats in a region is proportional to the area, A, of the region. Would it make sense to use differential equations to model the size of the population? If so, write the differential equation. If not, explain why.
1d) Assume the population, P, is changing at the rate proportional to (75-P). Does it make sense to use a differential equation to model the size of the population? If so, write the differential equation. If not, explain.
1e) If the rate of change, W, is inversely proportional to W and is always greater than 0. If W(0)=250 and W(2)=150, find the proportionality constant(k).
****PLEASE SHOW WORK**** I want to learn how to do these!
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1a) If the rate of change, W, is inversely proportional to W(x)
where W is always...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
Do the question completely. Especially part C thanks 4. A population P of organisms dies at a constant rate of a or...
Do the question completely. Especially part C
thanks
4. A population P of organisms dies at a constant rate of a organisms per unit time, and the growth rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) = Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The terms Po, a,...
please complete the whole question 4. A population P of organisms dies at a constant rate of a organisms per unit t...
please complete the whole question
4. A population P of organisms dies at a constant rate of a organisms per unit time, and the growth rate is proportional to the population size with the proportionality constant k A. Assume the initial population P(0) = Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answer must contain the terms Po,...
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumo...
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy (b) Solve the differential equation. Assume y(o) (c) A small town has 2100 inhabitants. At 8 AM, 100 people have heard a...
Q2- Fish Population In this question, we will use differential equations to study the fish population...
Q2- Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per year is P'(t): P'(t) birth rate - death...
Urgently need the answers. Please give right answers. Q2 Fish Population In this question, we will...
Urgently need the answers. Please give right answers.
Q2 Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate. Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per...
2. The growth rate of a population of bacteria is directly proportional to the population p()...
2. The growth rate of a population of bacteria is directly proportional to the population p() (measured in millions) at time t (measured in hours). (a) Model this situation using a differential equation. (b) Find the general solution to the differential equation (c) If the number of bacteria in the culture grew from p(0) = 200 to p(24) = 800 in 24 hours, what was the population after the first 12 hours?
Son 11 Name Write Equations for Proportional Relationships Study the example showing how to ident...
son 11 Name Write Equations for Proportional Relationships Study the example showing how to identify a proportional relationship. Then solve problems 1-9. Example The table shows the relationship between the money that Leo earns and the number of lawns that he mows. Is the relationship proportional? The ratios of the money earned to the number of lawns all simplify to y, or 5, so the relationship is proportional. Graph the relationship between the money earmed and the number of lawns...
3. A certain population of short lived insects is known to reproduce at a rate proportional...
3. A certain population of short lived insects is known to reproduce at a rate proportional to their current population. They are also known to reproduce at a rate proportional to the difference between the carrying capacity of their environment (the maximum population their envirnment can support) and their current population. The carrying capacity is proportional to their food supply, which changes with the season. The amount of food given in thousands of pounds is sin(t) + 2, where t...
Part B Please!! Scenario The population of fish in a fishery has a growth rate that...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
&7 4. A population P grows at a constant rate of a organisms per unit time, and the death rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answe terms Po, a, k and a constant C.) wer must contain the...
Do the question completely. Especially part C
thanks
4. A population P of organisms dies at a constant rate of a organisms per unit time, and the growth rate is proportional to the population size with the proportionality constant k. A. Assume the initial population P(0) = Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The terms Po, a,...
please complete the whole question
4. A population P of organisms dies at a constant rate of a organisms per unit time, and the growth rate is proportional to the population size with the proportionality constant k A. Assume the initial population P(0) = Po. Write a differential equation that models the size of the population P(t) at ay time t. B. Write the equation from part A in standard form, and solve. (The answer must contain the terms Po,...
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy (b) Solve the differential equation. Assume y(o) (c) A small town has 2100 inhabitants. At 8 AM, 100 people have heard a...
Q2- Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per year is P'(t): P'(t) birth rate - death...
Urgently need the answers. Please give right answers.
Q2 Fish Population In this question, we will use differential equations to study the fish population in a certain lake. An acceptable model for fish population change should take into account the birth rate, death rate, as well as harvesting rate. Let P(t) denote the living fish population (measured in tonnes) at time t (measured in year) Then the net rate of change of the fish population in tonnes of fish per...
2. The growth rate of a population of bacteria is directly proportional to the population p() (measured in millions) at time t (measured in hours). (a) Model this situation using a differential equation. (b) Find the general solution to the differential equation (c) If the number of bacteria in the culture grew from p(0) = 200 to p(24) = 800 in 24 hours, what was the population after the first 12 hours?
son 11 Name Write Equations for Proportional Relationships Study the example showing how to identify a proportional relationship. Then solve problems 1-9. Example The table shows the relationship between the money that Leo earns and the number of lawns that he mows. Is the relationship proportional? The ratios of the money earned to the number of lawns all simplify to y, or 5, so the relationship is proportional. Graph the relationship between the money earmed and the number of lawns...
3. A certain population of short lived insects is known to reproduce at a rate proportional to their current population. They are also known to reproduce at a rate proportional to the difference between the carrying capacity of their environment (the maximum population their envirnment can support) and their current population. The carrying capacity is proportional to their food supply, which changes with the season. The amount of food given in thousands of pounds is sin(t) + 2, where t...
Part B Please!!
Scenario The population of fish in a fishery has a growth rate that is proportional to its size when the population is small. However, the fishery has a fixed capacity and the growth rate will be negative if the population exceeds that capacity. A. Formulate a differential equation for the population of fish described in the scenario, defining all parameters and variables. 1. Explain why the differential equation models both condition in the scenario. t time a...
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